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BEPP 305/805:
Risk Management, Lecture 1 Professor Jeremy Tobacman
January 16, 2014
Goals
• Individuals and firms face risks in nearly all decisions that they make.
• Provide an introduction to decision making in a world with uncertainty. ▫ How should individuals, and managers of firms, make
decisions involving risk?
▫ What are the typical mistakes made in decisions involving risk?
2
Why study risk management?
• As an individual, you face risks in many aspects of your life.
• Managers of firms make many decisions that involve risks, and the consequences can be large.
• A lesson from the recent financial crisis: the failure to properly manage risk can result in disaster.
3
Lessons from the financial crisis
“The crisis spurred a remarkable degree of reflection and activity throughout the community. The unifying theme is a focus on risk management: the risks of a particular product or financial service, the risks to a firm, and the systemic risks to society as a whole.” - Retiring HBS Dean Jay Light on the recent developments in the curriculum
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“I believe that a CEO must not delegate risk control. It’s simply too important… ”
– Warren Buffet
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"Named must your fear be before banish it you can.“
– Yoda
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Structure of the course
1. Optimal decision making under risk (Tobacman)
2. Barriers to risk management (Wang)
3. Corporate risk management (Nini)
7
Module I in one slide
• Why is it important to account for risks?
• How is risk measured in practice?
• What is the optimal way to make decisions under risk?
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Module II in one slide
• Barriers to risk management
• Market impediments
▫ Information and incentive problems
• Psychological impediments
▫ People don’t always behave optimally
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Module III in one slide
• Corporate risk management
▫ When firms SHOULD NOT manage risk
▫ When firms SHOULD manage risk
▫ Strategies for corporate RM
▫ Managing liability risk
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Overview of the syllabus
• Course structure and requirements
• Prerequisites
• Course grading
• Policies for dropping/withdrawing
• Expectations
• Policies for exams
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Grading
• Three exams, one for each module.
• Problem sets, posted on Canvas
▫ Work in teams but write your own solutions ▫ Graded on a complete/incomplete system ▫ You can skip turning in one problem set with no penalty ▫ Module I due dates: 1/24, 1/31, 2/7 at 5:00pm
• Survey questions will also be posted on Canvas
• Problem sets and survey answers are worth 10% of your
grade
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Slides and notes
• Slides will be posted on Canvas
• Notes summarizing certain aspects of the course material will be posted on Canvas periodically, generally after the material is covered in class
13
One slide study guide
• Primary resources:
▫ Lectures
▫ Notes posted to Canvas
▫ Problem sets
• Readings are intended to be references
14
About me
• Assistant Professor in BEPP since 2008
• Ph.D. in Economics from Harvard
• Research on household finance for the poor
▫ Consumer credit in the US
▫ Microinsurance against rainfall risk in India
▫ Behavioral economics
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My info
• Office: 1409 SH-DH
• Email: [email protected]
• Office hours: Tuesdays 4:30-5:30pm or by appt
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TAs for the course
• Banruo (Rock) Zhou
• Ella Zhang
• Neil Iyer
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Practice Sessions
• Neil (1/21 & 2/4) - 4:30pm
• Rock (1/21 & 2/4) - 7:30pm
• Ella (1/22 & 2/5) - 4:30pm
• Attend the most convenient one
• Optional but awesome
• Rooms TBA
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Probability Theory
Rest of the lecture
1. Define what we mean by risk
2. Build up concepts of probability theory
3. Some methods for measuring risk
a. Variance as a measure of risk
b. Value at Risk
c. Mean-variance criterion
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An example
• A person retires at age 70, with a total of $1 million
• She expects to live for another 25 years
• How much can this person consume per year?
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An example
• A person retires at age 70, with a total of $1 million
• She expects to live for another 25 years
• How much can this person consume per year?
▫ Assume a real interest rate of 2% per year:
Approximately $50.22k per year
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Dollars remaining (in thousands)
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But, there is uncertainty!
• What if the person lives longer than 25 years?
• What if the interest rate falls?
• Calculations based on averages can be misleading
▫ Need to account for risk
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Another example
• A manager wants to estimate inventory costs for the business, based on inventory amount.
▫ If demand is lower than inventory: Unsold units spoil, entailing a $50 cost per unit.
▫ If demand exceeds inventory: Extra units must be air-freighted in, at a cost of $150 per unit.
• Monthly demand is, on average, 5,000 units per month.
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Understanding probabilities is crucial
• Given average monthly sales of 5,000, what are expected inventory costs if the manager decides to have monthly inventory of 5,000? • Zero?
• More than Zero?
• Cannot be determined? Source of this example: Harvard Business Review
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Understanding probabilities is crucial
• Expected inventory costs are greater than zero, if there is any variation in demand from month to month.
• Using averages can be very misleading!
• The appropriate method is to consider the whole probability distribution for demand, not just the average of the distribution.
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The “flaw of averages”
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One of many other examples
• In 1997, the U.S. Weather Service forecast that North Dakota’s rising Red River would crest at 49 feet.
• Official in Grand Forks made flood management plans using this single number, an average….
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One of many other examples
• In 1997, the U.S. Weather Service forecast that North Dakota’s rising Red River would crest at 49 feet.
• Official in Grand Forks made flood management plans using this single number, an average….
• The river crested above 50 feet, breaching the dikes.
• 50,000 people were forced from their homes, and there was $2 billion in property damage.
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What is risk?
• Very broadly, risk involves uncertainty
▫ Many possible outcomes
• Most decisions involve some degree of uncertainty
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Examples of risk
• Individuals
▫ Labor income, mortality, injuries, asset returns
• Firms
▫ Input costs, borrowing costs, demand, regulation
• Governments
▫ Unemployment, social security costs, business cycles, wars, commodity prices
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How can we model risk?
• Answer: Probability theory
• Provides us a way to think about what the most likely outcome is
• … and gives us a way to model the range of possible outcomes
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Some concepts
• Sample space
▫ Set of all possible things that can happen
• Probability distribution
▫ Relative chance that each state can occur
• Random variable
▫ Function that assigns outcomes to each state
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A simple example: a coin flip
• Sample space ▫ {H,T}
• Probability distribution
▫ {½, ½}
• Random variable, some examples ▫ X = Number of heads
X(H)=1. X(T) = 0
▫ Y = Number of tails Y(H)=0, Y(T) = 1
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Another example: two coin flips
• Sample space ▫ {HH, HT, TH, TT}
• Probability distribution
▫ {¼, ¼, ¼, ¼}
• Random variables ▫ X = number of heads
X(HH) =2, X(HT) = 1, X(TH) = 1, X(TT) = 0
▫ Y = proportion of heads Y(HH) = 1, Y(HT)= ½, Y(TH) = ½, Y(TT) = 0
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Probability distribution
Outcomes x1 x2 x3 x4 x5 x6
Pro
ba
bil
ity
p1
p2 p3
p4
p5
p6
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Properties of random variables
• Expected value
▫ Measure of the central tendency
• Variance and standard deviation
▫ Measures of dispersion
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Expected value (mean)
• Weighted average of outcomes
E X p1x1 p2x2 ... p
nxn
n
ii
xi
p
1
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Variance
• Expected squared deviation from the mean
2
222...
2211
XEXE
XEn
xn
pXExpXExpXVar
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Standard deviation
• Square root of the variance
▫ Same units as X
SD X( ) = Var X( )
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Variance and SD as measures of risk
• Var and SD measure the expected dispersion
between outcomes and the average outcome
• Higher when ▫ Outcomes can deviate a lot from expected value ▫ Probability of extreme deviations is high
• Let’s think about whether these are good measures of risk
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Example
• Investment A
▫ $0 with probability 2/3
▫ $9M with probability 1/3
• Investment B
▫ $-5M with probability 0.2
▫ $5M with probability 0.8
• Which is the riskier investment?
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Example
• Profit from Investment A
▫ $0 with probability 2/3
▫ $9M with probability 1/3
• Profit from Investment B
▫ $-5M with probability 0.2
▫ $5M with probability 0.8
Mean = 3M Variance = 18𝑀2 Mean = 3M Variance = 16𝑀2
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Asymmetry
• Var and SD potentially measure risk, but they miss something:
• Large losses are “more risky” than large gains
• Extreme example
▫ Worst case scenario
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Another way to quantify risk
• Value at Risk (VaR)
• Question:
▫ What is the minimum loss under exceptionally bad outcomes?
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Value at Risk (VaR)
• Minimum loss in the bottom p% of outcomes
▫ Focus on the left tail of the distribution
▫ Usually 1% or 5% for a given time interval
Pro
ba
bil
ity
1%
2% 3%
5%
VaR at 10% is -4
7.5%
VaR at 1% is -10 VaR at 5% is -6
Profit -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20
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Example
• Profit from Investment A: ▫ -$1M with probability 0.1% ▫ $0 with probability 49.9% ▫ $2 with probability 50%
• Profit from Investment B:
▫ -$1 with probability 20% ▫ $1 with probability 80%
• Which investment is riskier?
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Example
• Profit from Investment A: ▫ -$1M with probability 0.1% ▫ $0 with probability 49.9% ▫ $2 with probability 50%
• Profit from Investment B:
▫ -$1 with probability 20% ▫ $1 with probability 80%
• Which investment is riskier?
VaR at 1% = $0 VaR at 5% = $0 VaR at 10%= $0 VaR at 1% = -$1 VaR at 5% = -$1 VaR at 10%= -$1
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Mean-Variance Criterion
• Balancing expected tendency and variance
• aE(X)-bVar(X)
▫ a>0, b>0
• An investment in X might be preferred to Y if:
▫ a[E(X)]-b[Var(X)] > a[E(Y)]-b[Var(Y)]
▫ What does this say?
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Mean-Variance Criterion
• Basis of Markowitz’s (1950) portfolio theory ▫ 1990 Nobel Prize ▫ Often used in practical applications
• Prior to Markowitz, portfolios were chosen on the basis of E(X) alone, without regard for Var(X)!
• We will study the properties of the mean-variance criterion later in the course
51
Review of concepts: An example
• Random variable: damages from an automobile accident
Possible Outcomes for Damages Probability
$0 0.50
$200 0.30
$1,000 0.10
$5,000 0.06
$10,000 0.04
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Expected value
Possible Outcomes for Damages Probability
$0 0.50
$200 0.30
$1,000 0.10
$5,000 0.06
$10,000 0.04
EV = .5(0) + .3(200) + .1(1,000) + .06(5,000) + .04(10,000) = $860
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Variance
Possible Outcomes for Damages Probability
$0 0.50
$200 0.30
$1,000 0.10
$5,000 0.06
$10,000 0.04
Variance = .5(0-860)2 + .3(200-860)2 + .1(1,000-860)2
+ .06(5,000-860)2 + .04(10,000-860)2 = 4,872,400 ($2)
54
Standard deviation
Possible Outcomes for Damages Probability
$0 0.50
$200 0.30
$1,000 0.10
$5,000 0.06
$10,000 0.04
SD = (Variance) 1/2 = (4,872,400)1/2 = 2,207 ($)
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Practical concerns
• Where do these probabilities come from?
• We need a way to translate past observations into probabilities
▫ Statistics
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Summary of today’s class
• Inference based on samples averages can be quite misleading
▫ Need to account for risk
• Probability theory allows us to model risks A measure of a typical observation (mean)
Measures of expected dispersion (variance and SD)
(Imperfect) measures of risk
57
